<p>I'm prepping for the AP exam on wednesday, and I stumbled across this problem in the PR book.</p>
<p>A swimmer is at a point 500 m from the closest point on a straight shoreline. She needs to reach a cottage located 1800 m down shore from the closest point. If she swims at 4m/s and walks at 6m/s, how far from the cottage should she come ashore so as to arrive at the cottage in the shortest time?</p>
<p>I kept getting 1780 m but the book says ~1350m.</p>
<p>Could someone please verify and show the steps? Thanks!</p>
<p>i believe your book is incorrect b/c i get ~1130 (triple checked)</p>
<p>ok, i posted my poorly drawn, but otherwise correct drawing of the situation of the equation which puts distance/velocity for each to get an equation for time so we can find the minimum time</p>
<p>next, take the derivative of the equation (in a TI-89 perferably) and then find the critical points at which the derivative is equal to zero. in this case, it's the x coordinate 447.231 or so. Sub it back in and get about 670 for x and the distance from the cottage to be about 1130 m. </p>
